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Nonlinear physics and mechanics
Approximate Weak Solutions to the Vorticity Evolution
Equation for a Viscous Incompressible Fluid
in the Class of Vortex Filaments
O. S. Kotsur, G. A. Shcheglov, I. K. Marchevsky Bauman Moscow State Technical University,
ul. 2-ya Baumanskaya 5, str. 1, Moscow, 105005 Russia
Abstract:
This paper is concerned with the equation for the evolution of vorticity in a viscous incompressible fluid, for which approximate weak solutions are sought in the class of vortex filaments.
In accordance with the Helmholtz theorem, a system of vortex filaments that is transferred by
the flow of an ideal barotropic fluid is an exact solution to the Euler equation. At the same time,
for viscous incompressible flows described by the system of Navier – Stokes equations, the search
for such generalized solutions in the finite time interval is generally difficult. In this paper, we
propose a method for transforming the diffusion term in the vorticity evolution equation that
makes it possible to construct its approximate solution in the class of vortex filaments under
the assumption that there is no helicity of vorticity. Such an approach is useful in constructing
vortex methods of computational hydrodynamics to model viscous incompressible flows.
Keywords:
weak solution, vortex filament, helicity of vorticity, diffusion velocity, viscosity.
Received: 20.06.2022 Accepted: 05.08.2022
Citation:
O. S. Kotsur, G. A. Shcheglov, I. K. Marchevsky, “Approximate Weak Solutions to the Vorticity Evolution
Equation for a Viscous Incompressible Fluid
in the Class of Vortex Filaments”, Rus. J. Nonlin. Dyn., 18:3 (2022), 423–439
Linking options:
https://www.mathnet.ru/eng/nd803 https://www.mathnet.ru/eng/nd/v18/i3/p423
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Abstract page: | 88 | Full-text PDF : | 70 | References: | 24 |
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